GATE 2015 Civil Engineering

Consider the following statements for air-entrained concrete: (i) Air-entrainment reduces the water demand for a given level of workability (ii) Use of air-entrained concrete is re...

The smallest and largest Eigen values of the following matrix are : $$\left[ {\matrix{ 3 & { - 2} & 2 \cr 4 & { - 4} & 6 \cr 2 & { - 3} & 5 \cr } } \right]$$

For what value of $$'p'$$ the following set of equations will have no solutions? $$$2x+3y=5$$$ $$$3x+py=10$$$

Workability of concrete can be measured using slump, compaction factor and Vee bee time. Consider the following statements for workability of concrete: (i) As the slump increases,...

In a catchment, there are four rain-gauge stations, P, Q, R, and S. Normal annual precipitation values at these stations are 780 mm, 850 mm, 920 mm, and 980 mm, respectively. In th...

The composition of an air-entrained concrete is given below: Water : 184 kg /m 3 Ordinary Portland Cement(OPC) : 368 kg /m 3 Sand : 606 kg /m 3 Coarse aggregate : 1155 kg /m 3 Assu...

Consider the following differential equation $$x\left( {y\,dx + x\,dy} \right)\cos \left( {{y \over x}} \right)$$ $$\,\,\,\,\,\,\,\,\,\, = y\left( {x\,dy - y\,dx} \right)\sin \left...

The directional derivative of the field $$u(x, y, z)=$$ $${x^2} - 3yz$$ in the direction of the vector $$\left( {\widehat i + \widehat j - 2\widehat k} \right)\,\,$$ at point $$(2,...

Consider the following probability mass function (p.m.f) of a random variable $$X.$$ $$$p\left( {x,q} \right) = \left\{ {\matrix{ q & {if\,X = 0} \cr {1 - q} & {if\,X = 1} \cr 0 &...

The integral $$\,\int_{{x_1}}^{{x_2}} {{x^2}dx\,\,} $$ with $${x_2} > {x_1} > 0$$ is evaluated analytically as well as numerically using a single application of the trapezoidal rul...

The quadratic equation $${x^2} - 4x + 4 = 0$$ is to be solved numerically, starting with the initial guess $${x_0} = 3.$$ The Newton- Raphson method is applied once to get a new es...

The development length of a deformed reinforcement bar can be expressed as $$\left( {1/k} \right)\left( {\phi {\sigma _s}/{\tau _{bd}}} \right).$$ From the $$IS:$$ $$456$$-$$2000,$...

Consider the following complex function $$f\left( z \right) = {9 \over {\left( {z - 1} \right)\left( {z + 2} \right)}}.$$ Which of the following is ONE of the residues of the above...

The two columns below show some parameters and their possible values. Parameters Value P-Gross Command Area I-100 hectares/cumec Q-Permanent Wilting Point II-6℃ R-Duty of canal wat...

A groundwater sample was found to contain 500 mg/L total dissolved solids (TDS). TDS (in %) present in the sample is ________.

Let $$A = \left[ {{a_{ij}}} \right],\,\,1 \le i,j \le n$$ with $$n \ge 3$$ and $${{a_{ij}} = i.j.}$$ The rank of $$A$$ is :

The average surface area of a reservoir in the month of June is 20 km 2 . In the same month, the average rate of inflow is 10 m 3 /s, outflow rate is 15 m 3 /s, monthly rainfall is...

If the water content of a fully saturated soil mass is 100%, the void ratio of the sample is

A 588 $$cm^3$$ volume of moist sand weighs 1010 gm. Its dry weight is 918 gm and specific gravity of solids, G is 2.67. Assuming density of water as 1 gm/$$cm^3$$, the void ratio i...

Prying forces are

A superspeedway in New Delhi has among the highest super-elevation rates of any track on the Indian Grand Prix circuit. The track requires drivers to negotiate turns with a radius...

According to the concept of Limit State Design as per IS 456: 2000, the probability of failure of a structure is __________.

A column of size $$450\,mm \times 600\,mm$$ has unsupported length of $$3.0$$ $$m$$ and is braced against side sway in both directions. According to $$IS$$ $$456: 2000,$$ the minim...

A steel member ‘M’ has reversal of stress due to live loads, whereas another member ‘N’ has reversal of stress due to wind load. As per $$IS$$ $$800: 2007,$$ the maximum slendernes...

The two Eigen Values of the matrix $$\left[ {\matrix{ 2 & 1 \cr 1 & p \cr } } \right]$$ have a ratio of $$3:1$$ for $$p=2.$$ What is another value of $$'p'$$ for which the Eigen va...

$$\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {1 \over x}} \right)^{2x}}\,\,$$ is equal to

Four cards are randomly selected from a pack of $$52$$ cards. If the first two cards are kings, what is the probability that the third card is a king?

In Newton-Raphson iterative method, the initial guess value $$\left( {{x_{ini}}} \right)$$ is considered as zero while finding the roots of the equation: $$\,f\left( x \right) = -...

Given $$i = \sqrt { - 1} ,$$ the value of the definite integral, $$\,{\rm I} = \int\limits_0^{\pi /2} {{{\cos x + \sin x} \over {\cos x - i\,\sin x}}dx\,\,} $$ is :

Consider the following second order linear differential equation $${{{d^2}y} \over {d{x^2}}} = - 12{x^2} + 24x - 20$$ The boundary conditions are: at $$x=0, y=5$$ and at $$x=2, y=2...

For step-size, $$\Delta x = 0.4,$$ the value of following integral using Simpson's $$1/3$$ rule is ______

The probability density function of a random variable, $$x$$ is $$$\matrix{ {f\left( x \right) = {x \over 4}\left( {4 - {x^2}} \right)} & {for\,\,0 \le x \le 2 = 0} \cr { = 0} & {o...

A triangular gate with a base width of 2 m and a height of 1.5 m lies in a vertical plane. The top vertex of the gate is 1.5 m below the surface of a tank which contains oil of spe...

In a system, two connected rigid bars $$AC$$ and $$BC$$ are of identical length $$L$$ with pin supports at $$A$$ and $$B.$$ The bars are interconnected at $$C$$ by a frictionless h...

A simply supported reinforced concrete beam of length $$10$$ $$m$$ sags while undergoing shrinkage. Assuming a uniform curvature of $$0.004\,\,{m^{ - 1}}$$ along the span, the maxi...